(a) Write out the operation table for 8 on {1,3,5,7}, and convince your self that this is a group. (b) Let Un be the elements of Zn that have inverses with respect to n. Convince yourself that Un is a group under n. (c) Prove that the elements of Un are those elements aZn such that gcd(n,a)=1. You may use Theorem 11.4.9 in this proof